After doing a bit of Google searching I found the likely problem: the patch for security bulletin MS04-011 (hotfix KB835732), which has many known problems reported for Windows 2000, one of which is "your Windows 2000-based computer stops responding ... or your CPU usage for the System process approaches 100 percent". The slowdown problem is discussed in knowledge base article 841382 which describes the problem and says there is a hotfix available, but that you must contact Microsoft support to obtain the hotfix (potentially paying for the privilege). I e-mailed Dell (the manufacturer who installed the OS), but their auto-response wasn't terribly helpful so I had to wait for a technician's response.
However, a post over at utteraccess shows how to uninstall the bad patch in minutes. The key is raising the task priority of each system process that is required to uninstall the patch.
I got Dell's e-mail reply this morning, after fixing the problem last night, and Dell was utterly useless. They said they couldn't send me the hotfix, didn't mention anything about the fix I had found on my own, and instead just sent me a list of general Windows 2000 troubleshooting links. Sigh.
In case anyone else runs into the same problem I'm going to post the uninstallation instructions (from the discussion board) below.
"After installing Security fix KB835732, the SYSTEM.exe procress uses up 99% of CPU time, and makes the system non-responsive.
To uninstall it:
(1) Boot into Safe mode.
(2) Use Ctrl + Alt + Del to run TaskManager - and notice that the SYSTEM process is using 99% of the CPU time.
(3) From TaskManager set the Priority of the EXPLORER process to REALTIME (right-click it to get the context menu), so that you can get to the control panel.
(4) Run ADD/REMOVE PROGRAMS from control panel.
(5) Go back to TaskManager and set the Priority of MSHTA.exe to REALTIME, so that the ADD/REMOVE PROGRAM can get some CPU time.
(6) Select and Remove "Windows 2000 Hotfix - KB835732".
(7) Go back to TaskManager and set the Priority of "SPUNIST.exe" to REALTIME, for the uninstall program to run.
(8) Wait a few minutes, and the uninstall program will eventually ask you to click FINISH to reboot the machine. It may take a considerable amount of time.
(9) The machine should become normal after reboot."